Rough surface profiler and method

ABSTRACT

A method of profiling a rough surface of an object includes moving the object along a z axis so that a highest point of the rough surface is optically aligned with and outside of the focus range of a solid-state imaging array. An interferogram of the rough surface then is produced by means of a two beam interferometer. The solid-state imaging array is operated to scan the rough surface along x and y axes to produce intensity data for each pixel of the solid-state imaging array for a plurality of frames each shifted from the other by a preselected phase difference. The modulation for each pixel is computed from the intensity data. The most recently computed modulation of each pixel is compared with a stored prior value of modulation of that pixel. The prior value is replaced with the most recently computed value if the most recently computed value is greater. The object is incrementally moved a selected distance along the z axis, and the foregoing procedure is repeated until maximum values of modulation and corresponding relative height of the rough surface are obtained and stored for each pixel.

This is a continuation of patent application Ser. No. 08/048,747 filedApr. 16, 1993, by Donald K. Cohen et al., and entitled "ROUGH SURFACEPROFILER AND METHOD", which is a continuation of patent application Ser.No. 07/880,083 filed May 6, 1992 by Donald K. Cohen et al., and entitled"ROUGH SURFACE PROFILER AND METHOD" now U.S. Pat. No. 5,204,734 whichissued on Apr. 20, 1993, which is a continuation of patent applicationSer. No. 07/714,215 filed Jun. 12, 1991 by Donald K. Cohen et al., andentitled "ROUGH SURFACE PROFILER AND METHOD", now U.S. Pat. No.5,133,601 which issued on Jul. 28, 1992.

BACKGROUND OF THE INVENTION

The invention relates to an interferometric measuring device capable ofprofiling a surface with large height variations.

Conventional phase shifting interferometers require that the surface ofan object being profiled be quite smooth, so that continuousinterference fringes are produced by it. A large step change (i.e., aquarter of a wavelength of the light used to make the measurement ormore) in the height of the surface often destroys the continuity ofinterference fringes, and consequently conventional phase shiftingalgorithms executed by a computer in response to fringe intensity dataproduced by a solid-state imaging array, such as a CCD array, are unableto accurately compute the profile of the surface.

At the present time, measurement of accurate profiles of surface areasis limited to RMS average roughness of approximately one thousandAngstroms using single wavelength interferometric techniques. Usingmultiple wavelength techniques (such as those described in commonlyassigned U.S. Pat. No. 4,832,489, issued May 23, 1989, to Wyant et al.),surfaces with approximately one micron average roughness may bemeasured. With single wavelength techniques, the present state of theart limits measurement to surface step features of no greater heightthan approximately 0.16 microns. With multiple wavelength techniques,step height measurements are limited to steps less than approximately 15microns in height.

U.S. Pat. No. 4,818,110 (Davidson) discloses a Linnik Microscope incombination with a video camera, a wafer transport stage, and dataprocessing electronics, based on the use of an interference microscopeto measure height and width of surface features on an integratedcircuit. However, this reference does not disclose pixel-by-pixelmapping of the surface of a sample, does not generate a profile, and isincapable of generating an accurate pixel-by-pixel area profile of asurface that is too "rough" to be measured by conventionalinterferometry.

The article "Profilometry with a Coherent Scanning Microscope", by ByronS. Lee and Timothy C. Strand, Applied Optics, Volume 29, No. 26, Sep.10, 1990, discloses a "coherence scanning microscope" in which an objectis scanned in the z direction. White light interference fringes thatresult from the scanning are demodulated to find the peak amplitude ofan envelope of the fringes to determine the value of z at the peakinterference fringe. The Lee and Strand paper discloses no specific wayof demodulating the fringes, and indicates that ambiguities introducedby phase change on reflection due to dissimilar materials renders thetechnique inoperable. No interpolation techniques or curve fittingtechniques that might improve accuracy are disclosed. Optical pathdifference increments apparently are limited by the step size of steppermotors used, as is the speed of incrementing. The disclosed profile datais two-dimensional, rather than three-dimensional. The Lee and Strandreference clearly does not teach a technique to accomplish fast, highlyaccuracy surface profiling of surfaces having wide ranges of smoothnessor roughness, or of dealing with phase ambiguity errors that result fromphase change on reflection due, for example, to dissimilar surfacematerials.

Although phase-shifting techniques can produce measurements of surfaceroughness of the order of one thousandth of a wavelength, most presentmethods detect phase modulo 2π, and consequently give rise to errorssometimes referred to as "2π ambiguities" but hereinafter referred to as"phase ambiguities" or "phase ambiguity errors". Various kinds of "phaseunwrapping" algorithms are used to track the phase over a large range ofsurface heights and resolve the phase ambiguity errors. Problems arisewhen there is a height variation between two adjacent pixels that cannotbe unambiguously "unwrapped". The result is an integration error thatusually manifests itself as a streak across the field of view.

It is well known that different materials on a surface to be profiledproduce a phase shift known as "phase shift on reflection", whichintroduces phase ambiguity errors when conventional phase shiftingtechniques are utilized to determine the surface profile. Morespecifically, it is known that if the material of a surface beinginterferometrically profiled has optical properties such that theincident ray is delayed in phase by an appreciable amount, there will bea shift, i.e., by the "phase shift on reflection" in the phase of thefringe pattern received at the detector. Phase shifts which can causephase ambiguity errors also may occur when there is a thin transparentfilm on the surface being optically profiled, because the film addsdelay to the light propagation time therethrough.

There is an unmet need for an accurate, high speed, noncontact profilercapable of profiling a wide variety of rough surfaces.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the invention to rapidly produce anaccurate area profile of a rough surface having height variations thatexceed the focus range of conventional interferometric profilers.

It is another object of the invention to provide a method and apparatusfor accurate area profiling of a rough surface composed of differingmaterials which produce phase changes on reflection.

It is another object of the invention to provide a method and apparatusfor interferometrically profiling rough surface areas without the needto use a phase unwrapping algorithm.

It is another object of the invention to provide a method and apparatusfor interferometrically profiling rough surface areas very rapidly,without requiring excessive amounts of computer memory and algorithmexecution time.

It is another object of the invention to provide an improved apparatusand technique for real time demodulation of interference fringe signalsin an interferometric area profiling system.

It is another object of the invention to provide a method and techniquefor measuring surfaces with RMS average roughness of more thanapproximately one micron.

Briefly described, and in accordance with one embodiment thereof, theinvention provides a method of profiling a rough surface of an object byproducing an optical path difference so that initially a highest pointof the rough surface is optically aligned with and outside of the focusrange of a solid-state imaging array. Then an interferogram of the roughsurface is produced by means of an interferometer. The solid-stateimaging array is operated to scan the rough surface along x and y axesto produce intensity data for each pixel of the solid-state imagingarray for a plurality of frames each shifted in time from the previousone to vary the optical path difference by a preselected phasedifference. The contrast or modulation for each pixel is determined fromthe intensity data. That contrast or modulation is compared with astored prior value of contrast or modulation of that pixel. The priorvalue is replaced with the most recently computed contrast or modulationif the most recently computed one is greater than the one previouslystored. The corresponding relative height or optical path difference isalso stored for that pixel. The optical path difference is eitherincrementally or linearly varied through a selected distance, and theforegoing procedure is repeated until maximum values of contrast areobtained and stored for each pixel. In one embodiment, the modulation iscomputed from intensity data obtained during conventional phase-shiftinginterferometric measurements. In another embodiment, the phase is alsocomputed for each pixel from the intensity data and is used along withthe modulation to improve vertical resolution. In another embodiment,intensity data is "amplitude demodulated" using classical communicationstheory to extract an "envelope" of the intensity data and determine thepeak thereof. The envelope signal or modulation signal is "separated"from the "carrier" signal of the intensity waveform produced as thesolid-state imaging array passes through focus. The separation isaccomplished by a digital low pass filtering operation. The resultingseparated modulation signal is input to a digital correlator whichdetects the peak and correlates it to the surface height of the presentpixel.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of the rough surface profiler of the presentinvention.

FIG. 2 is a diagram showing an output signal that can be produced bydetector cells in FIG. 1 as the optical path difference is variedthrough the best focus point of the objective.

FIG. 3 is a simplified block diagram of another embodiment of theinvention.

FIG. 4 is a detailed block diagram of another embodiment of theinvention.

FIG. 5 is a flow chart useful in describing the operation of theembodiment of FIG. 4.

FIG. 6 is a diagram useful in explaining a phase interpolation techniqueto improve resolution of surface height measurements.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1, rough surface profiler 1 includes a Mirauinterferometer 2 having a reference mirror 2A on a glass plate 2B, and abeamsplitter 2C. A microscope objective 4 is supported above a testsurface 3 by a piezoelectric transducer (PZT) 5. PZT 5 is supported by aframe of Mirau interferometer 2. Mirau interferometer 2 is supported bythe frame of microscope section 1A. The vertical or z position ofmicroscope section 1A is controlled by a motor 60, which is connected bya mechanical link 60A to microscope section 1A. Test surface 3 issupported on a stage 66. The optical path difference (OPD) is preciselycontrolled by PZT 5 in response to PZT driver signal 59 produced bycomputer 30. Motor 60 is controlled by signal 63 produced by motorcontroller circuitry 58.

A white light source, which can be a typical quartz halogen lamp,directs white light through a typical commercially availableillumination assembly 7, which directs the white light beam onto anordinary beamsplitter 9. Beamsplitter 9 reflects the white light beam 10into the upper end of microscope objective 4.

The beams reflected from the reference mirror 2A and the sample surface3 then pass back up through microscope objective 4, upward throughbeamsplitter 9, through a collimating lens 31, and through amultilayer-coated beamsplitter 12 which deflects approximately 30percent of the interference beam 20 into eyepiece assembly 13. Most ofthe interference beam 20 continues upward through imaging lens 11 tosolid-state imaging array 18. Camera electronics 19 processes thesignals of the individual CCD (Charge Coupled Device) cells or othersolid-state imaging array cells of solid-state imaging array 18 andoutputs them via bus 27 to computer 30. Computer 30 communicates via bus28A with microcontroller 28.

Microcontroller 28 can be an Intel 8098. Block 68 includes a z joystickcontroller by means of which an operator can manually control motor 60to control the vertical position of microscope section 1A relative tosample surface 3, and is connected by suitable conductors 68A to inputsof microcontroller 28. Microcontroller 28 communicates by bi-directionalbus 28A with computer 30, which can be a desk-top computer incombination with a commercially available WYKO PMI (Phase MeasuringInterface). Microcontroller 28 generates outputs 57 which control motorcontroller circuitry 58. Microcontroller 28 and motor controllercircuitry 58 actually are included in the above WYKO PMI unit.

A filter may be positioned under solid-state imaging array 18 and camerascanning electronics 19. The signals produced by detector array 18represent profile of sample surface 3, and are scanned by camerascanning electronics in block 19 which produce amplified signals on bus27 that are digitized and input to computer 30 for suitable processingin accordance with the needs of the user.

The reference path and sample path in Mirau interferometer 2 areessentially identical except that the reference path is focused onmirror surface 2A and the sample path is focused on the test surface 3.Numeral 26 designates the vertical z axis of interference microscope 1.

The waveform shown in FIG. 2 is typical of those produced by theindividual CCD cells in detector 18 in response to light of theinterferogram impinging on detector array 18 as the optical pathdifference is changed. It is seen that this response is very peaked, andidentification of the ideal microscope objective focus point is quitedistinct. Dotted line 25 designates an "envelope" of waveform 23, whichin accordance with one embodiment of the invention, is extracted fromthe "carrier signal" using classical communications techniques to obtainthe "modulation" signal that is highest when the microscope objective isoptimally focused on the rough sample surface at the pixel underconsideration.

The image formed by a properly focused interference microscope typicallyconsists of a pattern of light and dark alternating interferencefringes. The number of fringes and the orientation of the fringes acrossthe image plane are dependent on the relative tilt between the samplesurface and the reference surface. Interference microscopes areassembled such that the brightest fringe occurs at "best focus" i.e.within the depth of focus of the microscope objective.

FIG. 3 shows a simplified diagram of a different embodiment of theinvention in which the stage 66, rather than the microscope objective,is vertically moveable in the z direction. Stage 66 is preciselymoveable, either linearly or in minute (e.g., 0.1 micron or less)increments in response to increment signals 59 from computer 30.

The specimen to be profiled has a "rough" surface 3, as in FIG. 1, thatexceed height variations which can be profiled by the closest prior artinterferometer-type surface profilers. Solid-state imaging array 18,which has an objective 4, is supported in a fixed position above stage66. Camera electronics 19 are connected by bi-directional bus 27 tosolid-state imaging array 18 to control scanning of rough test surface 3by the solid-state imaging array in camera 18 and to receive intensitydata from each pixel of the solid-state imaging array. Cameraelectronics 19 communicate with computer 30, mainly to supply measuredpixel intensity data to it. Computer 30 executes software that convertsthe data into a surface profile and may perform further analysisthereon, and displays the surface area profile and/or analysis resultson a screen, or outputs the data to control a plotter that plots thesurface profile. In FIG. 3, the elements of the interferometer thatproduce the fringe pattern (which results from interference betweensource light reflected from rough surface 3 and a reference surface)viewed by solid-state imaging array 18 are omitted, for simplicity. Theinterferometer hardware is similar to that shown in FIG. 1.

In accordance with the present invention, either stage 66 is lowered(FIG. 1) or microscope objective section 1A is raised (FIG. 3) so thatthe image of rough surface 3 is beyond the range of solid-state imagingarray 18. Then, computer 30 causes the OPD between solid-state imagingarray 18 and the rough surface 3 to be either reduced in minute (e.g.,0.1 micron) increments or reduced linearly and sampled at the sameincrements by controlling the position of stage 66. For each suchincrement, solid-state imaging array 18 scans rough surface of sample 3.The intensity data of the interference fringe pattern is sent tocomputer 30 after the intensity data has been converted to digital formby camera electronics 19.

Computer 30 then, for each pixel (i.e. , x-y location) scanned by thesolid-state imaging array 18, computes the modulation (or other suitableparameter) of that pixel, and compares it with the highest modulationstored so far for that pixel. If the new contrast or modulation ishigher than the prior highest stored modulation, computer 11 updates thestored highest modulation by replacing it with the new one, and alsostores the corresponding value of OPD or relative surface heightpresently being scanned.

After this has been accomplished for every pixel of solidstate imagingarray 30 for the present value of z, the OPD is, in effect, incrementedand the entire process is repeated. This happens many times, until theOPD or relative surface height variable z has changed enough to pass thebest focus point of objective 4 through the maximum possible heightrange of all of the rough surface features of rough surface 3 in thefield of view.

When the process is completed, computer 30 then has stored both themaximum contrast for each pixel and the value of z constitutes theprofile of the surface 3.

The advantage of the forgoing technique is that it does not require anycontinuity of fringes on steep, high step features of specimen surface3.

The general interference equation for the intensity measured in a 2-beaminterferometer is as follows:

    I=I.sub.0 [1+Mcos(φ+α)],

where I₀ is the DC bias term, φ is the initial phase angle, α is theincremental phase change, and M is the modulation.

Phase-shifting techniques usually make use of a narrow-band light sourceand assume that M is constant throughout the measurement. Multipleframes of data are taken while the OPD is varied by a known amountbetween each frame. The resulting group of above equations (1) then canbe solved using least-squares techniques or the like to determine thephase of each pixel at which the intensity is measured. The relativeheight at each pixel then is given by the formula ##EQU1##

The present invention makes use of the modulation information and theinterference data corresponding to each pixel at which the intensity ofthe sample is measured, and correlates that information to the relativesurface height of the sample at that pixel. If a broad bandwidth source,i.e., white light, is used instead of a filtered narrow bandwidth lightsource, the intensities of the fringes produced fall off sharply as theoptical path difference is varied, as indicated in FIG. 2.

If the assumption is made that the maximum value of modulation M occurswhen the OPD is near zero, then the position of the peak of themodulation function may be used to map the relative surface heightthroughout the field of view. The modulation function has the advantageof being non-periodic, and therefore will not have the above mentionedphase ambiguity errors.

It should be noted that measuring the modulation of fringes produced bya white light source is somewhat problematic. If standard phase-shiftingmethods are used to solve the basic interference equation for modulationM, the phase shift between frames must be very accurately calibrated.This becomes difficult due to spectral variations in the reflectivity oEthe sample and variations in the peak wavelength of the light source.The basic interference equation (1) assumes that the modulation isconstant with respect to z, which of course is not true for a whitelight source. The result is a very noisy modulation signal. Even so,respectable results were obtained on "very" rough surfaces using themethods described herein, because the modulation noise was smallcompared to the roughness of the surface.

In one experimental embodiment of the invention, phase information wasused along with modulation information to improve the resolution. Inanother (presently preferred) embodiment of the invention, "amplitudedemodulation" of the fringes was performed using techniques similar tothose used in AM radio receivers.

An initial attempt at profiling a rough surface used a stepper head andmotor-driven micropositioner as shown in FIG. 3 to produce relativetranslation of the test surface 3 along the z axis. Standardinterferometric phase-shifting techniques were used to obtain intensitydata used to compute the modulation. This first attempt proved thegeneral workability of the concept of focusing the microscope on eachpoint of the rough surface to obtain a surface map of values of z atwhich maximum modulation was computed for each pixel, but worked wellonly for very rough surfaces. A second attempt used computed phaseinformation, in addition to the computed modulation information, fromthe measured intensity data to improve measurement resolution. A thirdattempt, which seemed to produce the best results, used amplitudedemodulation techniques somewhat similar to those commonly used incommunications systems to decode the modulation function. These threeexperimental embodiments of the invention will now be described indetail.

The above-mentioned initial attempt to implement the invention usedhardware similar to that of FIG. 3, which is a simplified diagram that,for simplicity of illustration, omits the interferometer elements shownin FIG. 1. A vertical translating stage (a KLINGER P/N UZ80 PP) was usedto vary the OPD by moving the rough sample surface 3 through "focus"(i.e., the best focus point of microscope objective 4), as controlled bya Hewlett-Packard 330 microcomputer, through a programmable indexer (aKLINGER P/N CC-1.2). The assignee's commercially available TOPO 3Dversion 4.9 software, revised slightly to provide suitable control ofstage 66 and to make calculations described hereinafter, was used. Theassignee's standard TOPO five-frame phase-shifting algorithm was used tocollect five intensities I₁ -I₅ at each pixel for each OPD value. Theintensities were used to calculate the modulation M at each pixel inaccordance with the equation ##EQU2##

1₁ -I₅ are five consecutive frames of intensity data for every pixel,taken with relative phase shifts of π/2 between the frames, I₀ being theaverage light level, which is constant and need not even be used if thepurpose of the computations is to find the value of z at which themaximum modulation occurs.

Stage 66 (FIG. 3) was stepped at a 0.1 micron rate for a sufficienttotal scan length that the entire range of surface height of roughsample surface 3 could pass through focus. More specifically, at eachstep the piezoelectric transducer (PZT) 5 (e.g., see FIG. 1) wasshifted, and five frames of intensity data were taken. The value of Mwas calculated in accordance with equation (3) for each pixel, and thenwas compared to a previously stored value. For each pixel, if the newvalue of M was larger than the previously stored one for that pixel, thenew value of M was stored, along with the current z value. Thus, after acomplete scan, a complete profile of rough surface 3 consisting of therelative surface height of each pixel at which the maximum modulation orfringe contrast occurred was stored.

The resolution obtained for the above described initial experiment wasreasonably good, but not satisfactory. The experiment was repeated, butwith the "best focus" of each pixel being selected as the point at whichthe intensity for that pixel was maximum. However, the results were nobetter. The same experiments were performed for both filtered light andwhite light, using a standard GAR P/N S-22 for the purpose of evaluatingperformance of the device. The amount of time taken to execute the frameshifting algorithm was considered to be too long. Varying degrees of"noise" or error were present on smoother samples, although good resultswere obtained for the roughest samples, which had peaks of about 30microns.

In a second attempt to improve the resolution, phase information wasused in addition to the modulation M computed in accordance withequation (3), in the hope of obtaining better resolution than the 0.1 to0.6 micron resolution obtained for the above described embodiment of theinvention. The vertical distance between measurements was selected toequal approximately one eighth of the mean wavelength of the broadbandlight source. The equations used for 3-frame phase shifting with alinear ramping of the OPD with distance or time precisely producing 90degree phase shifts between frames, are as follows: ##EQU3##

The step size was calibrated for a phase shift of π/2. The algebraicsigns (i.e., + or -) of the numerator and denominator of equation (5)are used along with the modulation M of equation (4) calculated at eachstep, and the new modulation M is stored only if both signs are negativeand M is greater than the previous stored value. For this value of z,the phase is also calculated from the measured intensity values and alsostored with the current step number. This technique ensures that thepeak modulation M is always stored in the same quadrant along with thepeak of the fringe and that the phase calculated there will beindependent of the phase calculated at adjacent pixels.

The profile of the test surface 3 then is produced at the end of themeasurement by taking each stored "step number" (the step number is avariable that is incremented for each phase shift) and multiplying thatby the distance per step, and adding or subtracting an incrementaldistance from that using the corresponding phase data, as indicated byequation (6). This is done for each pixel scanned. The result is acomplete three dimensional map which is obtained without the need forphase discontinuity removal techniques, and thus is inherently free fromintegration errors.

The resulting resolution of this technique produced much higherresolution, almost as good as the assignee's TOPO 3D system, for smooth,flat surfaces. Measurement of rougher samples produced good resultssimilar to those obtained for the first-described technique. Moderatelyrough surfaces, however, sometimes produce measurements with randomspikes that occur at offsets of approximately 2π from surroundingfeatures. It is believed that these phase ambiguity errors resulted fromnot being able to reliably detect the peak fringe position, causing thecalculated z value to jump to the next fringe, a distance of 2π away.Some of these phase shifts are believed to be due to phase shift onreflection. Thin transparent or semi-transparent films (of thicknessless than a coherence length of the light source) also produce similarphase shifts. Although the foregoing technique produced very goodresults on "very" rough surfaces (e.g. , several microns RMS roughness), on "moderately" rough surfaces (e.g., 100 to 300 nanometers RMSroughness), it was clear that additional processing would be required todetect the peak fringe and that it would be necessary to continuallyrecalibrate the phase shift produced by PZT 5, as the accuracy of suchshifting was found to be critical.

Referring to FIG. 6, the above-mentioned improvement in resolution isaccomplished by "offsetting" the phase φ between intensity measurementpoints such as 88, 89 and 90 on the highest intensity fringe 23C ofintensity waveform 23. The highest intensity fringe 23C is previouslyisolated by using the peak of envelope 25 of intensity waveform 23Cshown in FIG. 2. Points 88, 89, and 90 indicate already measuredintensity points at phases spaced π/2 apart. The above-describedresolution problem is caused by the fact that none of intensitymeasurement points 88, 89, or 90 is located at the value of z at whichthe peak 23A is located. In order to get an accurate value of the righthand "phase offset term" in equation (6), the present invention involvescomputing values of M "on the fly" according to equation (4) usingintensities measured from points 88, 89, and 90 and storing that valueif both 1) it is the highest value of M computed so far, and 2) theterms (I₁ -I₂) and (I₃ -I₂) are both negative or one is negative and theother zero. When that condition is met, the phase offset term φ iscomputed according to equation (5), and is used to "adjust" or "refine"the more approximate value given by the left term of equation (6). Thislater term represents the peak of the modulation envelope 25 (FIG. 2).It should be noted that the actual phase of the peak modulation relativeto the height calculated using equation (6) is 3π/2, but since thisrelative offset is added to every pixel, the net result is the same.(Those skilled in the art know that the basic interference equation isequation (1), which has three unknown variables. Therefore, at leastthree measurements of intensity must be measured at different phases tosolve for the three unknown variables. Measurement of additional valuesof intensity at additional phases can, as a practical matter, furtherimprove accuracy of phase computation if the well known least squarestechnique is used to solve for the unknown variables.)

The above-mentioned third embodiment of the invention involved modifyingthe system of FIG. 1 so as to produce the system essentially as shown inFIG. 4. In FIG. 4, microcomputer system 30 includes a "frame processor"36, which can be a digital signal processor (DSP) board plugged into aback plane bus 37 of an IBM AT computer system. Vertical motion controlcircuitry and PZT control circuitry in block 38 also is connected to theinternal bus 37 and to digital signal processor 36. An 80X86 CPU 39 thatis connected to internal bus 37 is the main processor of microcomputersystem 30. An optional color video monitor 35 can be connected todigital signal processor and video interface circuit 36, for the purposeof effectuating real time video display.

Numeral 41 designates a conventional color monitor of microcomputersystem 30, to which keyboard 42, printer 43, and work station bus 40also are connected. The PZT control circuitry in block 38 produces alinear ramp signal 45 that drives a PZT amplifier 50, which can be aconventional amplifier such as the one used in the assignee'scommercially available TOPO 3D system. PZT amplifier 50 produces a highvoltage PZT drive signal on conductor 53 to control a PZT (not shown)that is used to increment the fine vertical translator 71, which isshown in FIG. 4 as being "nested" in a coarse vertical translator 70.(OPD variation can, of course, also be produced by incrementing thestage 66 in the z direction.) Coarse vertical translator 70 is driven inresponse to a circuit shown in block 55, which can be an "autofocus"printed circuit board contained in the assignee's commercially availableTOPO A/F system. The coarse position control signal on conductor 61controls coarse vertical translator 70.

The relative position of test surface 3 and optical system 18 ismeasured by a conventional linear variable differential transducer(LVDT) 73 or the like, which produces signals on conductor 74 and inputsthem to LVDT signal conditioning or buffer circuitry 51. LVDT signalconditioning circuit 51 produces an output signal which is applied as aninput to PZT amplifier 50, and also supplies an encoded voltage onconductor 52 to the PZT control circuitry in block 38. The encodedvoltage on conductor 52 represents the precise position of thesolidstate imaging array 18 relative to the present pixel of roughsurface 3. Dotted line 76 designates an optical coupling betweensolid-state imaging array 18 and rough surface 3.

LVDT signal conditioning circuit 51 produces very precise feedback inthe form of encoder voltage 52 indicating the present position of theobjective of solid-state imaging array 18. PZT control circuitry inblock 38 adjusts the ramp signal on conductor 45 so that solid-stateimaging array 18 moves very linearly. The PZT control circuitry in block38, PZT amplifier 50, PZT included in fine vertical translator 71 ofFIG. 4, LVDT 73, and LVDT signal conditioner 51 function as a servocircuit that maintains the translation or variation of the OPD preciselylinear.

Waveform 23 in FIG. 2 is of the same general shape for each of theintensity signals produced at the outputs of each of the pixels ofsolid-state imaging array 18 as the OPD is incrementally or linearlyramped so that the microscope objective 4 scans through the entire rangeof rough surface features of test surface 3. This waveform can beconsidered to be analogous to an ordinary AM radio signal. Waveform 23of FIG. 2 is defined by the above interference equation of equation (1)

    I=I.sub.0 +I.sub.O o+Mcos(φ+α).                  (1)

It is useful to compare this equation to the equation for an amplitudemodulated rf signal, used in radio communications:

    s(t)=[1+m(t)]Ucos(2πft+α),

where s(t) is the product of a modulating signal s(t)=1+m(t) and asinusoidal carrier signal Ucos(2πft+α), where U is a constant. The twoequations (1) and (7) are very similar, with the optical interferencesignal of equation (1) offset by the DC term I₀. Those skilled in theelectronic communications art know that amplitude modulation isgenerally defined as a linear operation where a frequency translation ofa modulating signal is performed by multiplication of the signal by asinewave carrier. Amplitude demodulation is a reverse operation, i.e.,the reconstruction of the modulating signal from the modulated signal.The technology for accomplishing this is well known to those skilled inthe communications art.

It was hoped that the same demodulation techniques that apply toclassical AM detection theory would apply to obtaining the modulationenvelope 25 and "detecting" its peak to profile rough surface 3.

A basic operation that must be accomplished to make the above-mentionedamplitude demodulation technique work in the present invention is theseparation of the modulation signal from the carrier signal in thefrequency domain by use of a low pass filter. For example, in an AMradio, the low pass filtering is typically accomplished by using asimple RC network. However, the filtering of the fringe intensity databecomes more complicated, due to the fact that the intensity datathrough focus for each pixel is not available as a continuous analogsignal, as in the case of an AM radio, but instead is sampled anddigitized once each video frame.

Therefore, a digital technique must be used to perform the low passfiltering function. One possibility to accomplish the low pass filteringwould be to perform a Fourier transform on the data collected for eachpixel for an entire measurement and then perform "computationalfiltering" in the Fourier domain. This approach would require storing alarge number of frames of video data, thereby imposing massive memoryrequirements on the system. Another possibility for performing the lowpass filtering would be to use a digital filter algorithm to calculate anew filter output at each step (i.e., at each OPD) of the profilingprocess. The amount of memory required then would be reduced to oneframe of video data for each "order" of the filter. The higher the orderof the filter, the steeper its cutoff characteristics are, indicatingbetter separation of the modulation envelope and the carrier signal. Thedetails of the design are common knowledge, and are selected from pages218 to 223 of "Digital Signal Processing" by J. V. Oppenhiem and R. W.Schafer, Prentice-Hall, New Jersey, 1975.)

The flow chart of FIG. 5 shows the operation of "extracting" ordetecting the "envelope" 25 of waveform 23 in FIG. 2. The peak of theenvelope 25 then corresponds to the point of best focus, and thereforecorrelates to the relative height of the present pixel of rough surface3.

The intensity data obtained from the phase shifting operation is shownin FIG. 5 as an input to block 80, in which the sampled intensity dataI(n) is stripped of the DC component I₀, by use of either a digital highpass filter or by subtracting an average DC value from the intensitysignal produced by each pixel (by digital low pass filtering oraveraging techniques).

As shown in block 82, the resulting signal x(n), then is "rectified" toperform the needed frequency separation. The rectification process in anAM radio typically is implemented using a simple solid state diodecircuit. However, to rectify the signal in a digital or time-sampleddomain, a non-linear operation such as taking an absolute value orperforming a mathematical squaring or the like must be applied to thediscrete data. The result is a signal r(n) that now has the frequencycomponents of the modulation signal moved to a lower frequency, whilethe frequency components of the fringes have been multiplied by a factorof 2 in the frequency domain.

The modulation signal M(n-N), where N is the "order" of the filter, thencan be separated by the digital low pass filtering operation, asindicated in block 84 of FIG. 5. This modulation signal M then is inputto a correlator that detects the peak (and/or other features) of themodulation signal M and correlates the feature(s) to the relativesurface height z of the present pixel, as indicated in block 86.

For the initial implementation of a so-called IIR (infinite impulseresponse) digital filter (which is preferred because it generally willlead to a simple implementation and require far less memory space forstorage of the delay terms than an FIR (finite impulse response filter),a fourth order Chebyshev design with a cutoff frequency of approximately0.2π was chosen.

The algorithm executed to implement the above digital filter is asfollows. First, the intensity signal from the detector is averaged foreight frames at the beginning of a measurement, during which time thedata points all remained above "focus", i.e., outside the coherencelength of the light source. The PZT stage 5 (FIG. 1) or other OPDtranslating technique in effect moves rough surface 3 through "focus" ata fixed rate, and the data is taken at fixed time intervals such thatthe distance moved between frames is approximately 50 nanometers.

After the eight frames of intensity data are taken for each pixel ofsolid-state imaging array 18, the average of the eight frames iscompuoted and subtracted from each intensity value obtained throughoutthe measurement. At this point the delay terms (4 frames) are cleared,and the signal can begin to be input to the digital filter. Meanwhile,the PZT continues to ramp at the same rate of 50 to 100 nanometers perstep.

The above technique involving averaging the first eight frames isperformed for the purpose of obtaining the "DC" value I₀ referred topreviously. That I₀ then is subtracted from each intensity valueobtained during the measurement process in order to obtain a signal withno DC component. Alternatively, the same objective can be achieved byfiltering the intensity signal using a digital high pass filter with aform similar to the low pass filter described above.

The DC-subtracted signal then is rectified by one of two methods, bytaking the absolute value of the data or by squaring the data. Themethod to be used is selected by the user at the start of eachmeasurement. The rectified signal then is input to the fourth order IIRlow pass digital filter described above. At each step after the fourth,a new value of modulation is output for each pixel.

The modulation calculated by the filter then is compared with themaximum modulation computed up until that step, and if the current valueis greater than the previous value, the current value is stored alongwith values computed at the previous steps. This requires the storing ofthe last three frames of modulation output for all pixels. The stepwhere the maximum modulation occurred also is stored.

After the measurement is complete, interpolation by quadratic fitting isperformed on three points saved for each pixel, to determine the actualsurface height at that point. If the three modulation values taken inthe vicinity of the peak of the modulation function are Y₁, Y₂, and Y₃,with Y₂ being the highest value of the three, three equations can bewritten relating each point to a point on a quadratic equation:

    y=a.sub.0 +a.sub.1 z+a.sub.2 z.sup.2                       (8)

where z₁, z₂, and z₃, are relative positions or offsets from theposition of the peak value, with z₁ =-1, z₂ =0, and z₃ =1.

The three equations can be solved for the three unknowns a₀ a₁ and a₂,and the expression for the interpolated offset from z₂ to the positionof the peak modulation value is given by the expression ##EQU4##

The result then is multiplied by the step size to obtain the relativeheight of the present pixel of the rough surface 3.

The above digital filter algorithm was used to test a wide variety ofrough surfaces, and much better results were obtained than for the firsttwo approaches described above. No phase ambiguity offset errors wereobserved, and no errors due to phase shifts (for example due to presenceof thin films or phase shift on reflection), were observed. Measurementresolution of less than 10 nanometers was achieved. The technique workedwell over a wide range of PZT ramp signal slopes, source illuminationlevels, source filtering, etc. No recalibration of PZT ramp signal slopewas necessary for different sample types.

It therefore was concluded that the use of digital filtering algorithmsis a very robust technique, the performance of which can be furtherimproved by better filter design, better DC tracking (which can beaccomplished by the above-mentioned high pass filtering), and more"intelligent" peak detectors.

In another embodiment of the invention, relative height values for thevarious pixels of rough surface 3 that correspond to the peak ofmodulation envelope 25 can be used to eliminate the phase ambiguityerrors from the height measurement for each pixel. By determining thepeak of the modulation envelope, the described digital filteringtechniques, in combination with the described phase measurementtechniques, it is possible to obtain better resolution of the surfaceprofile. The peak of modulation envelope 25 indicates a "coarse"measurement resolution, and the phase measurement technique providesadditional more accurate measurement values which, in accordance withthe second term of equation (6), are added to the initial measurement toprovide increased resolution. Thus, relatively smooth surfaces can bevery accurately profiled using the disclosed phase measurementtechniques, and very rough surfaces can be very accurately profiledusing the described modulation techniques. The immediately foregoingpeak modulation "interpolation" techniques allow measurement of surfacesof "intermediate" roughness with approximately the same resolution ascan be obtained in profiling very rough surfaces by combining bothtechniques sequentially in accordance with equation (6). That is, themodulation envelope peak measurement technique is first used to get arough measurement, and then the phase measurement technique is used tofurther refine that measurement.

The present invention thus provides a means of using a combination ofinterferometric techniques to make fast area measurements veryaccurately of surfaces of any degree of smoothness or roughness.

While the invention has been described with reference to severalparticular embodiments thereof, those skilled in the art will be able tomake the various modifications to the described embodiments of theinvention without departing from the true spirit and scope of theinvention. It is intended that all combinations of elements and stepswhich perform substantially the same function in substantially the sameway to achieve the same result are within the scope of the invention.

What is claimed is:
 1. A method of profiling a surface of an object,comprising the steps of:(a) positioning the object along an optical axisso that the object surface is optically aligned with an imaging device;(b) producing an interference pattern of the object surface by means ofan interferometer; (c) varying an optical path difference between theobject and a reference surface of the interferometer; (d) operating theimaging device to scan the object surface to produce intensity data foreach pixel of an image of the object surface; (e) removing a constant orslow-changing component from the intensity data, as the optical pathdifference is varied, to produce a first digital signal; (f) rectifyingthe first digital signal to produce a second digital signal including ahigh frequency component and a low frequency component; (g) digitallyfiltering the second digital signal to eliminate the high frequencycomponent from the second digital signal to thereby produce a thirddigital signal; (h) locating a preselected characteristic of the thirddigital signal for each pixel; and (i) correlating the preselectedcharacteristic of the third digital signal to a relative height of theobject surface for each pixel.
 2. A device for profiling a surface of anobject, comprising in combination:(a) an imaging device; (b) means formoving the object along an optical axis so that a portion of the objectsurface is optically aligned with the imaging device; (c) aninterferometer, and means for producing an interference pattern of theobject surface by means of the interferometer; (d) means for operatingthe imaging device to scan the object surface to produce intensity datafor each pixel of an image of the object surfacei. means for measuring aposition value corresponding to the relative distance between the objectsurface and a reference surface in the interferometer and producing aposition signal representing the position value, ii. means for applyingthe position signal as position feedback to a control circuit driving atranslator connected to vary the relative distance between the objectsurface and the reference surface, and iii. means for operating thecontrol circuit in response to the position signal to precisely linearlyadjust the relative distance between the object surface and thereference surface; (e) means for computing information representative ofvariations in amplitude of intensity for each pixel from the intensitydata; (f) means for comparing a most recently computed value of theinformation for each pixel with a stored prior value of the informationfor that pixel; (g) means for replacing the prior value of theinformation with the most recently computed value of the information ifthe most recently computed value of the information is greater than theprior value of the information; (h) means for obtaining and storing acorresponding relative height of the object surface if the most recentlycomputed value of the information is greater than the prior value of theinformation; and (i) means for varying the relative distance between theobject surface and the reference surface until maximum values of theinformation and corresponding relative heights of the object surface areobtained and stored for each pixel, respectively.
 3. A device forprofiling a surface of an object, comprising in combination:(a) animaging device; (b) means for moving the object along an optical axis sothat the object surface is optically aligned with the imaging device;(c) an interferometer, and means for producing an interference patternof the object surface by means of the interferometer; (d) means foroperating the imaging device to scan the object surface to produceintensity data for each pixel of an image of the object surface,includingi. means for measuring a position value corresponding to therelative distance between the object surface and a reference surface inthe interferometer and producing a position signal representing theposition value, ii. means for applying the position signal as positionfeedback to a control circuit driving a translator connected to vary therelative distance between the object surface and the reference surface,and iii. means for operating the control circuit in response to theposition signal to precisely linearly adjust the relative distancebetween the object surface and the reference surface; (e) dataprocessing circuitry adapted to remove a constant or slow-changingcomponent from the intensity data, as the optical path difference isvaried, to produce a first digital signal; (f) means for rectifying thefirst digital signal to produce a second digital signal including a highfrequency component and a low frequency component; (g) means fordigitally filtering the second digital signal to eliminate the highfrequency component from the second digital signal to thereby produce athird digital signal; (h) means for locating a preselectedcharacteristic of the third digital signal for each pixel; and (i) meansfor correlating the preselected characteristic of the third digitalsignal to a relative height of the object surface for each pixel.
 4. Adevice for profiling a surface of an object, comprising incombination:(a) an imaging device; (b) means for moving the object alongan optical axis so that the object surface is optically aligned with theimaging device; (c) an interferometer, and means for producing aninterference pattern of the object surface by means of theinterferometer; (d) means for operating the imaging device to scan theobject surface to produce intensity data for each pixel of an image ofthe object surface, includingi. means for measuring a position valuecorresponding to the relative distance between the object surface and areference surface in the interferometer and producing a position signalrepresenting the position value, ii. means for applying the positionsignal as position feedback to a control circuit driving a translatorconnected to vary the relative distance between the object surface andthe reference surface, and iii. means for operating the control circuitin response to the position signal to precisely linearly adjust therelative distance between the object surface and the reference surface;(e) means for determining a preselected characteristic of the intensitydata for each pixel; and (f) means for correlating the preselectedcharacteristic to a relative height of the object surface for eachpixel.
 5. A method of profiling a surface of an object, comprising thesteps of:(a) positioning the object along an optical axis so that theobject surface is optically aligned with the imaging device; (b)producing an interference pattern of the object surface by means of aninterferometer; (c) operating an imaging device to scan the objectsurface to produce intensity data for each pixel of an image of theobject surface, byi. measuring a position value corresponding to therelative distance between the object surface and a reference surface inthe interferometer and producing a position signal representing theposition value, ii. applying the position signal as position feedback toa control circuit driving a translator connected to vary the relativedistance between the object surface and the reference surface, and iii.operating the control circuit in response to the position signal toprecisely linearly adjust the relative distance between the objectsurface and the reference surface; (d) computing informationrepresentative of variations in amplitude of intensity for each pixelfrom the intensity data; (e) comparing a most recently computed value ofthe information for each pixel with a stored prior value of theinformation for that pixel; (f) replacing the prior value of theinformation with the most recently computed value of the information ifthe most recently computed value of the information is greater than theprior value of the information; (g) obtaining and storing acorresponding relative height of the object surface if the most recentlycomputed value of the information is greater than the prior value of theinformation; and (h) varying the relative distance between the objectsurface and the reference surface until maximum values of theinformation and corresponding relative heights of the object surface areobtained and stored for each pixel, respectively.
 6. A method ofprofiling a surface of an object, comprising the steps of:(a)positioning the object along an optical axis so that [a predeterminedfeature of]the object surface is optically aligned with the imagingdevice; (b) producing an interference pattern of the object surface bymeans of an interferometer; (c) operating an imaging device to scan theobject surface to produce intensity data for each pixel of an image ofthe object surface, byi. measuring a position value corresponding to therelative distance between the object surface and a reference surface inthe interferometer and producing a position signal representing theposition value, ii. applying the position signal as position feedback toa control circuit driving a translator connected to vary the relativedistance between the object surface and the reference surface, and iii.operating the control circuit in response to the position signal toprecisely linearly adjust the relative distance between the objectsurface and the reference surface; (d) removing a constant orslow-changing component from the intensity data, as the optical pathdifference is varied, to produce a first digital signal; (e) rectifyingthe first digital signal to produce a second digital signal including ahigh frequency component and a low frequency component; (f) digitallyfiltering the second signal to eliminate the high frequency componentfrom the second digital signal to thereby produce a third digitalsignal; (g) locating a preselected characteristic of the third digitalsignal for each pixel; and (h) correlating the preselectedcharacteristic of the third digital signal to a relative height of theobject surface for each pixel.
 7. A method of profiling a surface of anobject, comprising the steps of:(a) positioning the object along anoptical axis so that the object surface is optically aligned with theimaging device; (b) producing an interference pattern of the objectsurface by means of an interferometer; (c) operating an imaging deviceto scan the object surface to produce intensity data for each pixel ofan image of the object surface, byi. measuring a position valuecorresponding to the relative distance between the object surface and areference surface in the interferometer and producing a position signalrepresenting the position value, ii. applying the position signal asposition feedback to a control circuit driving a translator connected tovary the relative distance between the object surface and the referencesurface, and iii. operating the control circuit in response to theposition signal to precisely linearly adjust the relative distancebetween the object surface and the reference surface; (d) determining apreselected characteristic of the intensity data for each pixel; and (e)correlating the preselected characteristic to a relative height of theobject surface for each pixel.
 8. A device for profiling a surface of anobject, comprising in combination:(a) an imaging device; (b) aninterferometer producing an interference pattern of the object surface;(c) a microcontroller adapted to operate the imaging device to scan theobject surface to produce intensity data for each pixel of an image ofthe object surface, the microcontroller includingi. a positiontransducer adapted to measure the relative distance between the objectsurface and a reference surface in the interferometer and producing aposition signal representing the relative distance, ii. a circuitreceiving the position signal, producing position information inresponse to the position signal, and utilizing the position informationto control a translator control circuit driving the translator in orderto precisely linearly adjust the relative distance between the objectsurface and the reference surface; (d) the microcontroller being adaptedto correlate a preselected characteristic of the intensity data to arelative height of the object surface for each pixel.
 9. The device ofclaim 8 wherein the transducer includes a linear variable differientialtransducer.
 10. A device for profiling a surface of an object,comprising in combination:(a ) an imaging device; (b) an interferometerproducing an interference pattern of the object surface; (c) atranslator adapted to move the object along an optical axis of theinterferometer to vary an optical path difference between the objectsurface and a reference surface; (d) a control circuit adapted tooperate the imaging device to scan the object surface to produceintensity data for each pixel of an image of the object surface; (e)digital processing circuitry adapted to perform computations on theintensity data to remove a constant or slowchanging component from theintensity data as the optical path difference is varied, to produce afirst digital signal; (f) a rectifier rectifying the first digitalsignal to produce a second digital signal including a high frequencycomponent and a low frequency component; (g) digital processingcircuitry adapted to perform computations on the second digital signalto eliminate the high frequency component from the second digital signalto thereby produce a third digital signa, to locate a preselectedcharacteristic of the third digital signal for each pixels and tocorrelate the preselected characteristic of the third digital signal toa relative height of the object surface for each pixel.